Problem: Find the distance between the points (-4, -5) and (-9, 6). ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-4, -5)$ $(-9, 6)$ $5$ $11$
Explanation: Change in $x$ -4 (-9) Change in $y$ (-5) 11 The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{5^2 + 11^2}$ $= \sqrt{146}$